descriptive_analysis

Descriptive Statistics

Overall, expenditure on education per pupil has increased slightly in real USD.

When looking at the share of expenditure on elementary education coming from own sources (as opposed to state or national sources) we see a mean of 38.6%.

The following plot displays each county’s time series of expenditure (total and per pupil log values).

Key Relationships (KR)

Below are scatterplots and diagrams depicting key relationships between dependent and control variables as well as shares/components of key variables.

KR 1: Revenue Sources

Most important to tease out before modelling is how different revenue sources (federal, state, county (own), and other local sources) interplay. County-level revenue for public education is a combination of both local and intergovernmental sources. The local portion of the share is almost entirely sourced through property taxes. The intergovernmental sources come from state, federal, and local aid.

Below chart plots CZ-level mean (taken over the panel time horizon) of different intergovernmental (IG) sources versus own-source revenue (generated from local sources). The solid black line represents a best-fit line and the dashed line represents a 45 degree line. The blue plot shows Total IG Revenue (Federal + State + Other Local) versus own revenue. There is a near-1:1 negative correlation between the two (ie. they are near-substitutes for one another). This effect is dominated by State IG revenue (as can be seen in the purple panel). Propoerty taxes have a near 1:1 relationship with own revenue confirming that property taxes make up own revenue sources almost completely.

The following plots show the share of revenue for public education that comes from own sources, local intergovernmental, state intergovernmental, and federal intergovernmental by state. Almost all states have a near 50% split of revenue from state and own sources, which aligns with data from the Congressional Research Service cited in the Transfer of Status report. Massachusetts has an unusually high share of local IG support (inter-school aid), eclipsing own sources almost completely. From further research, I believe this has to do with a unique structure of Massachusetts public school funding which is reliant on several multi-county funding agencies (similar to the mentioned ESAs). This anomaly might warrant the exclusion of MA from the analysis.

The below plot provides the same information as above but on a national level.

Conclusion: Corroborates the near-even split of revenue between state and own sources which seems to be a fact of public education revenue. I mainly include this as an alternative summarising figure to the above.

KR 2: Revenue, Expenditure and Property Taxes

We know the majority of “own source” revenue comes from property taxes. The below scatterplots demonstrate the relationship between education revenue and expeniture versus property taxes collected. The solid black line represents a best-fit line and the dashed line represents a 45 degree line (intercept-adjusted to match data). The vertical dotted line represents a potential preliminary cutoff point for outliers - will be subject to further more rigorous testing.

KR 3: GDP and Property Taxes

The solid black line represents a best-fit line and the dashed line represents a 45 degree line.

GDP and Property taxes have a positive linear correlation, to be expected.

KR 4: GDP and Education Expenditure

The solid black line represents a best-fit line and the dashed line represents a 45 degree line (intercept-adjusted to match data).

GDP and Education expenditure have a positive linear correlation, as expected.

KR 5: Economic Diversity

If we use a Chmura economic diversity indicator and plot GDP, private industry GDP, education expenditure, and elementary education expenditure we see that there is little difference in the mean of expenditure, however higher values of each occur only in more diverse counties. This data is only available at county level, not commuting zone level.

KR 6: ESAs and County Expenditure

Around 2007, many states instituted Educational Service Agencies (ESAs) which sought to “equalise” public education across the country. To date, ~45 states have ESAs which are responsible for multiple school districts, most often across multiple counties. Therefore, when modelling county-level expenditure it will be important to understand how this change in educational expenditure affected county-level spending (ie. did ESAs replace or supplement county-level funding).

Only 593 counties of 2740 in the dataset have recorded revenue/expenditure from ESAs. After some digging, I believe that these values for ESAs are improperly recorded in the sense that the revenue is recorded only in counties in which the ESA’s headquarters is located and not partitioned to the counties to which the revenue ultimately flows. All county-level total expenditure/revenue values that are used in the regressions on this page have explicitly excluded recorded ESA values for this reason (they are instead recorded in a variable called esa_tot_exp or esa_tot_rev in total and per pupil values).

The below graphs show some relationships between ESA and county-level finances. I have yet to arrive at a definitive understanding of how ESAs and county-level finances interact. They do not appear to be substitutes. As is evident, the data on ESA expenditure is patchy and highly volatile by county. At the moment, I believe this is because of imperfect/inconsistent reporting in comparison to traditional school district reporting. The four states that have recorded ESA expenditure before 2007 are California, Illinois, Minnesota, Oregon.

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With this we want to demonstrate how ESAs interact with our expenditure indicator. Does high ESA spending imply low/high local spending? It seems from the below that the two have a no correlation, implying little substitution? (Each point is a county in a particular year starting from 2007, colour represents state). Warm color-scale is (top-left panel) is expenditure values whereas the cool color scales are revenue values. The black line is a 45 degree line.

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KR7: Expenditure per pupil and enrollment numbers

There might be a scaling law at play in the behavior of expenditure per pupil (expenditure per pupil declines as enrollment numbers decline). There are a few ways to control for this: simply add enrollment numbers (per CZ) as a regressor (suffers from the fact that aggregated up at a commuting zone level might lose heterogeneity in the CZ); control for enrollment/number of schools (need to create new variable for n_schools).

Dataset coverage

In this sanity check, I look at what proportion of reported school age children per state seem to be represented in the enrollment numbers in our Survey of Local Finances dataset. We see that this share varies in magnitude by state (Maine having only 40% of school-age children covered). Considering that ~ 9% of students are enrolled in private schools across the US, the coverage in the top states is not too bad!